Pick Your Poison

  ‘Archie really should be tucked up in his crib,’ said Elaine, ‘but Ruby insisted he would love it. I didn’t think it was such a good idea, but I trust her 100%.’ She shrugged. ‘After all, she was right about the baby food.’

  A few blocks away, Ruby and her friends were about to take their places on their Rigors of Mortis Square float. Red Monroe’s mother, Sadie, had finished making final adjustments to their costumes and everyone was ready to go.

  Red, who was having the best birthday of her entire actual life was particularly thrilled with everything, and even the fact that there were three other Rigors of Mortis Square floats didn’t tone down her delight.

  ‘We got the original costumes,’ she said as she hopped from foot to foot in her shiny black Cordelia Rigor tap shoes.

  ‘And we got a real baby,’ said Elliot. ‘No one else has a real Baby Grim.’ He glanced at Ruby. ‘How did you even get him?’

  ‘Just used my powers of persuasion,’ said Ruby.

  They all looked down at Archie Lemon.

  And he peered back at them from his large Victorian bonnet and gurgled.

  ‘He’s kinda cute, isn’t he?’ said Del. ‘Especially with that little moustache.’

  ‘Yes,’ said Ruby, ‘the moustache is an improvement.’

  ‘Thanks for showing up,’ said Del, giving Ruby a friendly pinch to her cheek.

  ‘How could I pass up the chance to have my head stuck under your armpit?’

  ‘You know your make-up is super realistic,’ said Red. ‘How did you achieve such a perfect black eye?’

  ‘I got someone to punch me,’ said Ruby.

  ‘You’re very dedicated,’ said Clancy.

  ‘So are you,’ said Mouse, ‘I mean, you really got into character.’ She was referring to the fact that Clancy was playing the part of Edgar Mortis who tragically died when bitten by a snake.

  ‘What can I say,’ said Clancy, ‘I’m a method actor.’

  ‘Too bad about Bug,’ said Elliot. ‘What are we going to do now we don’t have a dog to play Toadstool?’

  But that was about to change.

  ‘Hey Ruby, it’s me, I’m here.’ A ghost was waving at her and it was holding a leash. ‘And look, I got Dorothy with me!’ Quent Humbert was impossible to recognise, covered as he was in a bedsheet, but his little black pug dog Dorothy was very clearly dressed to play Toadstool.

  Ruby found herself giving Quent Humbert, if not a hug exactly, then a head-butt; it wasn’t easy to hug when you no longer had a body, and in any case, she probably wouldn’t actually have hugged Quent. Ruby reserved her hugs for the rare few.

  ‘You know Quent, I have to say, sometimes you’re not such a bedsheet.’

  ‘Yeah,’ said Clancy, ‘and who else could rustle up a levitating pug?’

  There was a loud bang and a flurry of fireworks to signal the start of the parade and slowly the float began to move.

  The parade had been going for no more than forty minutes when something dramatic happened: the wind suddenly picked up, catching bunting and orange lanterns, pulling them from their fixings and sailing them into the sky. And as the parade rolled on, the gusts grew stronger and pieces of costume were snatched and whirled into the night. It was only when someone shouted ‘tornado!’ that people began diving for cover.

  A funnel of wind appeared and twisted across the skyline. It moved at such speed that there was little time to do much but run this way and that.

  Pageant-goers watched from a distance as it tore through West Twinford making matchwood of houses before losing its power and disappearing altogether.

  A few houses in the Cedarwood Drive area were victims of the storm and one of these was the Lemons’ place, though the only part of their home that had been truly destroyed was the room where Archie Lemon slept.

  Had he not been playing the part of Baby Grim, the ghostly infant, at 7.23pm on the 31st of October, then he would have been sucked into the wind funnel and taken high into the dark sky, never to be seen again.

  The Lemon was a lucky kid.

  BABY GRIM SAVED FROM GRIM END

  Last night’s tornado could have claimed a tiny victim. ‘Had it not been for our babysitter, our nine-month-old son would have been abducted by a twister,’ said thirty-two-year-old mother of one, Elaine Lemon. She went on to say, ‘Ruby is like his guardian angel. If she had not insisted on taking him to the Halloween pageant last night, we would never have seen Archie again.’

  ENDANGERED-SNAKE PROTECTOR OUT OF DANGER

  Amarjargel Oidov finally came out of her coma last night. She has only a sketchy memory of the events that led to her poisoning and says she has no light to shed on the question of why anyone might wish her dead. She has requested that well-wishers kindly do not send her flowers.

  SNAKE BITE EPIDEMIC

  There have been an unusual number of snake-bite incidents in Twinford this past October and herpetologists can only put it down to changing weather patterns. ‘Nests of vipers have been turning up here, there and everywhere,’ said snake wrangler, Ralf Erwin. ‘If you see one, back away,’ was his advice. The public has been warned to keep off wasteland after Ambassador Crew’s son Clancy (thirteen) suffered a severe bite to his arm.

  DOG PREDICTS TORNADO

  Ten-year-old Old English Sheepdog, Bessie, saved her owner’s life when she prevented him from leaving the house. Seventy-four-year-old Al Budget was planning to drive to the supermarket, but his dog Bessie had other ideas. ‘When I picked up my car keys, she started growling at me in this real spooky type of way, and as I approached the door, she tripped me up, took me clean off my feet, then she just plum came and sat on top of me. There was nothing I could do, she’s a big dog, weighs about sixty to sixty-five pounds.’

  MATHLYMPICS MAYHEM

  Mathematics prodigy Dakota Lyme has been requested to partake in anger management classes after she attacked another contestant at the Yuleton Mathlympics quarterfinals. Dakota Lyme became so enraged when she lost out to eleven-year-old Ward Partial that she began hurling protractors, set squares and other geometry-based tools at him. Ward, though shaken, did not sustain any critical injuries.

  STOP PRESS: MIRROR READERS PRAISE NEW LOOK

  The Twinford Mirror launched its exciting new-look format to rave reviews. ‘I’ve never seen anything like it in Twinford before,’ exclaimed one regular reader, adding, ‘Come to think of it, it’s identical to the Twinford Echo.’

  Despite being back in everyone’s good books, Ruby Redfort still had one last task to complete. She had requested that her final stint of community service should be spent clearing the trash from the vacant lot where the Sacred Heart Cathedral had once stood.

  Sabina for one applauded her daughter’s efforts to keep Twinford tidy and thought it might be nice if the Twinford Garden Committee planted some roses. ‘Red ones, like hearts,’ said Sabina.

  Brant Redfort said he would speak to the Twinford Historical Society to see if it might be possible to open the crypt to the public. ‘I’m sure Dora Shoering would enjoy taking tour groups down there.’

  Mrs Digby said she was happy for the Sacred Heart’s dead to be remembered, but there was no way in a month of Sundays that anyone was getting her to visit them.

  Ruby shivered at the very thought, but didn’t say anything.

  It was after she had completed her task, eight and a half hours later, and was wondering what should be done with the Dime a Dozen shopping cart she had found, that an idea hit her.

  She walked it all the way from College Town back to Amster, stopping only to buy a tin of cat food. This done, she continued on her way to Cedarwood Drive. When she reached Mrs Beesman’s house, she parked the cart in front of her gate and placed the cat food in the basket. Then she went on home to Green-Wood house, where she was looking forward to taking a long, hot soak in the tub.

  The apple was sitting on Ruby’s desk, the bruise deepening and the rot spreading. She looked at it for a long while, wondering what it mea
nt, if indeed it meant anything.

  Finally she took her penknife and plunged it deep into the fruit. And a strange thing happened: the knife sliced the apple in two, and out fell a piece of folded white paper.

  Taking it up in her hand she opened it and read it.

  There was only one word, a name.

  She thought about the very last thing the Count had said: the question is: who pulled the trigger?

  She looked back down at the paper and read the name out loud.

  What it said was:

  LB.

  THINGS I KNOW:

  ..................

  The Australian is working for the Count.

  The Count is working for someone.

  The Count has betrayed this someone.

  This someone has a grand plan.

  This someone wants to kill me.

  Lorelei wants to kill me.

  LB killed Bradley Baker.

  THINGS I DON’T KNOW:

  ..........................

  WHY to all of the above.

  Where my mom’s snake earrings are.

  Ruby Redfort.

  by Marcus du Sautoy, supergeek consultant to Ruby Redfort

  Ruby discovers that the key to decoding the Taste Twister code is the geometry of a 4-dimensional cube. But what on earth is a 4-dimensional cube? We live in a 3-dimensional universe – seeing the objects around us in terms of their height, width and depth – so it’s impossible to see something that lives in four dimensions. Instead we must use some mathematics to conjure up this shape in our mind.

  The key to creating a 4-dimensional cube is the discovery that you can change geometry into numbers, and numbers into geometry. For example, every position on the surface of the earth can be located by two numbers. Ruby uses this fact to find out that the Taste Twister poster points to the Little Seven Grocers. She takes the two numbers written on the Taste Twister billboard and changes these numbers into a location.

  Called latitude and longitude, these two numbers are like a code to locate any place on the earth. For example, the Little Seven Grocers is located at the position given by the two numbers:

  (32.7410, -117.1705)

  These are known as the GPS coordinates of this location. The first number tells you how many units north or south you must go from the equator. The second number tells you how many units east or west you should travel from the line of longitude running through Greenwich in London. (From the equator to each pole consists of 90 units, corresponding to the 90 degree angle between the equator, the centre of the earth and each pole.)

  So, for example, the coordinates of my college in Oxford, New College, are (51.7542, -1.2520). So you can get to New College by going 51.7542 units north of the equator and 1.2520 steps west. If you want to find out the coordinates of your house then try putting your address into: http://www.gps-coordinates.net/

  It was the great French mathematician and philosopher René Descartes, born in 1596, who came up with this clever way of changing a geometrical location into numbers. Called Cartesian coordinates, they can be used to plot all kinds of things – not just locations on earth. You can describe any geometric shape using these coordinates. If you take a piece of graph paper with a shape drawn on it then we can change the shape into the numbers that tell us the location of the points making up that shape.

  For example, how can I change a square into numbers? What I do is tell you the location of all four corners of the square.

  The corners of the 2D square are located at the positions (0,0), (1,0), (0,1) and (1,1). The geometry of the square has been translated into these four pairs of numbers. (When describing shapes using Cartesian coordinates, the first number, called the x-coordinate, tells you how many units to move left or right, the second coordinate, called the y-coordinate, tells you how many units to move up or down. Beware: it is the opposite order to GPS coordinates.)

  But we don’t just have to stick to using two numbers. Ruby could also have added a third coordinate to the location of the Little Seven Grocers, telling us how high up from sea level the shop is. Using these three coordinates we can then describe the location of any point in our 3-dimensional universe.

  We can also use the same idea to change 3D shapes into numbers. If we want to describe a 3-dimensional cube in coordinates, instead of a square, then we can add a third direction which describes the height of the point above the 2-dimensional graph paper.

  The corners of the 3D cube are located at the positions (0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 0), (1, 0, 1), (0, 1, 1) and finally the point furthest from the first corner, located at (1, 1, 1). So the geometry of the cube has been translated into these eight triples of numbers.

  Descartes’ idea of changing geometry into coordinates is a bit like a dictionary changing words from English into French. But this dictionary changes shapes into numbers. On the shapes side of the dictionary, we have seen 2D shapes and 3D shapes, but then the dictionary runs out because we can’t draw a shape in 4D. But the exciting thing is that the numbers side of the dictionary doesn’t run out. It was the great German mathematician Bernhard Riemann, born in 1826, who discovered that you could carry on building shapes out of numbers, even if you couldn’t see them.

  What Riemann realised is that you could use the numbers to describe what a shape was made of, despite being unable to physically build it. All you needed to do was add more coordinates. So to describe a 4-dimensional object, we just add a fourth coordinate that will keep track of how far we are moving in this new imaginary direction. So although I can never physically build a 4-dimensional cube, by using numbers I can still describe it precisely.

  It has 16 vertices, starting at (0,0,0,0), with edges extending to 4 points at (1,0,0,0), (0,1,0,0), (0,0,1,0) and (0,0,0,1) and then continuing along the edges we hit points at (1,1,0,0), (1,0,1,0), (1,0,0,1), (0,1,1,0), (0,1,0,1), (0,0,1,1), (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) until we reach the farthest point, at (1,1,1,1). This 4D cube is sometimes known as a Tesseract.

  The numbers are a code to describe the shape, and we can use this code to explore the shape without ever having to physically see it. So, using the numbers, we can actually work out that, in addition to the 16 corners, this 4D cube has 32 edges, 24 square faces, and is made by putting together 8 cubes.

  Sometimes people talk about time being the fourth dimension, but actually these dimensions can be used to keep track of anything. For example, suppose you wanted to keep track of the temperature at every location on the earth. You could use three coordinates to locate the position and the fourth coordinate to tell you the temperature at that point.

  In the Taste Twister code, the four different directions keep track of the four different tastes we can detect with our tongues: BITTER, SOUR, SALT, SWEET. Every taste turns into a point located somewhere on this 4-dimensional cube.

  Although we can never actually see a 4D cube, there are ways to fake a view, as Ruby showed in her mathlympics competition. For example, the picture I drew of the cube isn’t actually a cube. It’s a 2D picture of the 3D cube. The great breakthrough by artists like Leonardo da Vinci in the fifteenth century was the idea of perspective – a way to draw 3D shapes on a 2D canvas to give you the illusion of seeing a scene in 3D. So for example, one way to draw a 3D cube on a 2D canvas might be to draw a large square with a smaller square inside, then join up the corners. This gives you the illusion of ‘seeing’ a 3D cube.

  Shadows work the same way. If I took a cube made out of wire and shone a light on the shape, then the 2D shadow I would see on the floor might look like the square inside a square.

  Just as you can paint a 3D shape on a 2D canvas or shine a light on a 3D shape and create a 2D shadow, there is a way to create a shadow or picture of a 4D shape in 3 dimensions. A 3D cube when squashed into 2D became a square inside a square. It turns out that the shadow of a 4D cube in 3 dimensions is a small cube inside a larger cube where there are extra edges inserted to join the points of the large cube to the
points of the smaller cube. This is the picture that Ruby draws in the final round of the mathlympics competition.

  If you ever go to Paris then you can actually see an example of this 3D shadow of a 4D cube. At La Défense in Paris there is a huge structure called La Grande Arche built by Danish architect Johann Otto von Spreckelsen. It is essentially a large cube with a smaller cube inside with the corners of the cubes joined up. If you visit La Grande Arche and count carefully, you can see the 32 edges that can be described using Descartes’ coordinates.

  But every shape has many different shadows. If I take my 3D wire cube and I alter the position of the torch, I can get different 2D shadows or perspectives. This is the breakthrough Ruby makes with the mandala shape on the back of the labels on the Taste Twister bottles.

  By taking different perspectives on a 4D cube, you can get different 3D viewpoints. (An animation showing these changing shadows of the Tesseract can be seen here: https://commons.wikipedia.org/wiki/File:8-cell.gif.) The mandala shape that is the key to decoding the locations of the taste code is arrived at by turning the 4D shape and getting a new perspective. You can actually see the two cubes still in the mandala shape. One is highlighted in the figure below. The other is obtained by shifting this cube down and right.

  The mandala image is actually a 2D picture of a 3D shape which is itself a shadow of a shape in four dimensions.

  And if your brain isn’t smoking by now then maybe you could be the next Ruby Redfort or Bernhard Riemann.

  Footnotes

  Chapter 5. Loose ends

  fn1 IF YOU WANT TO IMPROVE YOUR EYESIGHT THEN YOU SHOULD DRINK THIS.

  Chapter 32. The littlest recruit